1

Game Theory & Applications

Ian Larkin & Evan RawleyMBA 299: StrategyApril 15th, 2004

2

Agenda for today

Hand back case write-ups

Round 5 of the CSG

Game theory and applications

3

Grading philosophy and approach

1st pass to establish independent grade

2nd pass to ensure rank order is right

3rd read for anyone on the margin

Grades matter – I take them seriously

My strong presumption is that you will write very intelligent papers

Grading is more lenient on mid-term work than on the final

Final typically makes up a lot of the variability in grades

Philosophy Approach

4

Grades20: Outstanding 10-15%19: Very strong analysis; no major flaws 10-

20%18: Very good analysis w/clear thesis; some problems 10-

20%17: Good analysis overall; at least one major issue 25-35%16: Some good analysis, but at least 2 major problems 10-

20%<15: A few good points, but problems tend to dominate

<10%

Very good performance overall The only time a letter grade will be assigned is for your final course

grade

5

Thinking ahead to the finalWE NEED MORE OF: Establishing an organization

or framework for analysis that supports a thesis

Work on quant. Analysis More of it + going deeper Better justifications for

assumptions Deeper thinking about

dynamics Consistent logic Clarity around predictions

WE NEED LESS OF: Summarization of case facts Mechanical/exhaustive

application of “standard” frameworks

Bullet pointed lists Approaching it as “building

a business plan” rather than analyzing a case

Exhibits without quantitative analysis (save these for the boardroom)

6

Agenda for today

Hand back case write-ups

Round 5 of the CSG

Game theory and applications

7

Update on CSG 4 rounds complete; round 5 due by Monday at noon

Round 5 is THE MOST important round of the game!

Why? You have to decide where you’re going to play in the second half, and you have MUCH more info than you did when you made your initial decision in Round 1

8

Am I on a path to make money? If you had done nothing, by end of Round 5 you

would have had in the bank $1,000,000*(1.02)^4= $1,082,500

You’ll have to re-spend your capacity costs to “play” in the remaining rounds, so in order to be “on track” to make money, you should have MORE THAN$1,082,500 – .5*(total EC spent)

in the bank by the end of Round 5

Question: Why is this calculation simplistic?

9

You should do better in Rounds 6-9 It’s not unexpected that few teams will have the “break even”

amount of money in the bank at the end of Round 5. Rounds 6-9 are the chance to take advantage of what you gained in the earlier rounds: Have better information Sent signals to competitors, Reinvested along the way Hopefully won’t make as many mistakes

Most teams do STILL have the chance to beat “break even” which is $1,000,000*(1.02)^8=$1,172,000

10

Thinking about Round 6-9 strategyIf you DIDN’T make money in a market, why would you choose to rebuild your factory?

You expect fewer entrants in Round 6 (Why?) You expect better pricing in Rounds 6-9, even with the same

number of entrants (Why?) You expect the Magic CSG Fairy to bless your team

Staying in a market because you’re “committed” to it is NOT a valid reason

Assuming you lost money in your initial market in Rounds 1-5, a big part of your CSG memo needs to be why you did (or didn’t) choose to rebuild capacity for Rounds 6-9

11

Additional thoughts Some teams are doing very well! Can you figure

out who? What happens in the real world when there are “profit pools” out there? Does it make sense to go after them?

If you’re one of the “lucky ones,” did you capture as much value as you could have? What will you do if you are attacked?

12

Agenda for today

Hand back case write-ups

Round 5 of the CSG

Game theory and applications

13

What is game theory? Game theory is about how individual

decisions are made strategically by taking into consideration the actions and interests of competitors

What isn’t game theory: Much of traditional operations management Neo-classical micro-economics

Game theory is usually most applicable when there are limited numbers of players

14

Some Examples Areas where game theory can (has) been

fruitfully applied: Price competition between oligopolists Entry decisions Product differentiation and marketing decisions

Areas that are not game theory Optimizing factory line performance Monopoly pricing (maybe)…

15

Why is game theory useful? Provides predictions for what should happen

This means using estimates of payoffs to deduce behavior in advance

Explicitly considers what other players’ strategies are (or are likely to be), making it a more dynamic view than traditional economics

Moves away from the world of post-modern strategy where “anything goes” and much is rationalized ex-post

16

What is a game?Four elements

Players Payoffs (or Outcomes) Choices Rules

Given all of this information players try to determine what their best course of action should be given:

The possible actions they can take What they think other players will do What their payoffs are

Nash equilibrium occurs when all players have taken the previous factors into account and take their actions

17

A Simple Game: The Prisoner’s Dilemma

0,0 4,-3

1,1-3,4

Confess

Don’t Confess

Confess Don’t Confess

A

B

Three Key ComponentsPlayers Outcomes Choices

18

Nash Equilibrium of the Prisoner’s Dilemma (AKA what should everyone do)

0,0 4,-3

1,1-3,4

Confess

Don’t Confess

Confess Don’t Confess

A

B

Nash Equilibrium: Given what the other guy doing, you can’t do better

19

Application of Prisoner’s Dilemma: Price War

0,0 4,-3

1,1-3,4

Fight

Accommodate

Fight Accommodate

A

B

20

A few comments & caveats Equilibria are not necessarily socially

efficient; they are just in some sense “stable” Do we ever see inefficient equilibria in real life?

Better outcomes for the players could be achieved through coordination and commitment Mergers Collusion

21

Coordination Games: Divide the Market

-1,-1 1,3

-1,-13,1

Segment A

Segment B

Segment A Segment B

A

B

22

Coordination Games: Divide the Market

-1,-1 1,3

-1,-13,1

Segment A

Segment B

Segment A Segment B

A

B

23

Some examples of the coordination games & prisoner’s dilemmas Prisoner's dilemma

Pricing decisions when there are only a few firms

Coordination games Timing of advertisements on TV/radio Entry into (CSG) markets

These games differ in the amount of commitment required and what communication can get you in terms of outcomes

24

What about repeated games?What happens when we play the price war game over and over again?

0,0 4,-3

1,1-3,4

Fight

Accommodate

Fight Accommodate

A

B

25

Equilibrium in repeated playConsider the strategy: If you fought last round I will fight forever . . . If you accommodated in the last round I will accommodate until you fight

Assume no discounting for simplicity

4+0+0+0+0 . . . . =4

1+1+1+1+1 . . . . =n

26

Thinking about price wars Why do price wars stop?

PV (nice payoffs) > PV (bitter competition)

Why do price wars start?How do you credibly signal commitment to fight forever?

What happens if it’s not an infinite game? Would you ever cooperate?

27

Sequential games In sequential games, players move in a pre-

determined order, and can observe moves of other players that happened before they move

This type of game is useful in developing predictions in situations where one firm moves first and others follow Firms with a dominant player (e.g., AB/Bud advertising) Capacity decisions (e.g., Nutraweet) Patent games (e.g., Pharmaceuticals)

28

Capacity Expansion and Entry is one relevant example An established manufacturer is facing

possible competition from a rival The established retailer can try to stave off

entry by engaging in a costly capacity expansion, which increases supply and lowers price charged to customers

Rival can observe whether incumbent expands capacity or not before deciding on entry

29

Strategies

Incumbent: Expand capacity or not

Rival: Enter or not

30

Game Tree

I

R

R

1,1

3,2

2,4

4,2

Expand

Do notexpand

In

Out

In

Out

31

Game is solved using Backward Induction Look to the end of the game tree and prune

back Rationality assumption implies that players

choose the best strategy at each node There’s no incomplete information in this

game, so there’s no uncertainty in the prediction

32

What will rival do?

I

R

R

1,1

3,2

2,4

4,2

Expand

Do notexpand

In

Out

In

Out

33

Rival’s Choice

I

R

R

1,1

3,2

2,4

4,2

Expand

Do notexpand

In

Out

In

Out

34

What will incumbent do?

I

R

R

1,1

3,2

2,4

4,2

Expand

Do notexpand

In

Out

In

Out

35

Incumbent’s Choice

I

R

R

1,1

3,2

2,4

4,2

Expand

Do notexpand

In

Out

In

Out

36

Equilibrium Prediction The prediction from this model is that the

incumbent will expand capacity and this will effectively forestall entry

Notice that even in absence of actual entry, the potential competition from the rival eats into the incumbent’s profits. By thinking dynamically, game theory allows a

refinement of the typical economics monopoly prediction of MR=MC

37

Is Flexibility an Advantage? Preceding game assumed rival could move at

the last moment, after seeing incumbent’s decision

Suppose that the rival is less flexible in its management practices.

It must commit to enter or not before the capacity expansion decision of the incumbent.

How does this affect the outcome of the game?

38

Game Tree – Rival moves first

R

I

I

1,1

4,2

2,3

2,4

In

Out

Expand

Not expand

Expand

Not expand

39

Backwards Induction – Rival moves first

R

I

I

1,1

4,2

2,3

2,4

In

Out

Expand

Not expand

Expand

Not expand

40

Equilibrium Prediction

The absence of flexibility on the part of the rival improves its outcome relative to the case where it retained flexibility.

This game has a first-mover advantage Sometimes “flexibility to commit” is more

important than “flexibility to wait and see” Is it always true in sequential move games

that there is a first-mover advantage?

41

Defining the Rules Properly is Critical: An Example of What Can Go Wrong

Buy

Join

Join

Join

Join

Abstain

Abstain

Abstain

Abstain

Don’t buy

0,0,0,0,0

1

2

3

4

5

-10,0,0,0,0

0,0,0,0,0

2,2,2,0,0

4,4,4,4,0

6,6,6,6,61=B2=U3=T4=S5=E

What do you think happened?

42

Next time

More sophisticated game theory

More on repeated games

Cournot vs. Stackelberg games